5. Further Applications of Integration (a) Find the centroid of the region bounded by the curves…

5. Further Applications of Integration (a) Find the centroid of the region bounded by the curves y = 9 In 2x, y = 0, and x = { (b) Find the volume of the solid obtained by rotating the region from part (a) about the x-axis. () A telephone wire hanging between two telephone poles takes the shape of a catenary with equation y =C+acosh Suppose the two telephone poles are 50 ft apart, and the length of the wire between them is 51 ft. If the lowest part of the wire is to be 20 ft above the ground, how high up on each pole should the wire be attached?